Determination of the number of hidden units from a statistical viewpoint

One of the important problems for 3-layered neural networks (3-LNN) is to determine the optimal network structure with high generalization ability. Although this can be formulated in terms of a statistical model selection, there remains a problem in applying traditional criteria for 3-LNN. We suggest the type of effective criteria for the model selection problem of 3-LNN by analyzing the statistical properties of some simplified nonlinear models. Results of numerical experiments are also presented.